1. Field of the Invention
The present invention relates to the technical field of the oil industry, and more particularly the operation of subterranean reservoirs, such as oil reservoirs or gas storage sites.
2. Description of the Prior Art
Optimizing and operating oil pools rely on a description that is as accurate as possible of the structure, of the petrophysical properties, of the fluid properties, and so on, of the pool being studied. For this, the experts use a tool which makes it possible to reflect these aspects in an approximate manner known as the reservoir model. Such a model is a model of the subsoil, representative both of its structure and of its behavior. Generally, this type of model is represented on a computer, and it is then called a digital model. A reservoir model comprises a meshing or grid, usually three-dimensional, associated with one or more maps of petrophysical properties (porosity, permeability, saturation, etc.). The association process entails assigning values of these petrophysical properties to each of the meshes of the grid.
These models are well known and widely used in the oil industry, making it possible to determine numerous technical parameters relating to the study or operation of a reservoir, of hydrocarbons for example. In practice, since the reservoir model is representative of the structure of the reservoir and of its behavior, the engineer uses, for example to determine the areas that have the greatest chances of containing hydrocarbons, the areas in which it may be advantageous/necessary to drill an injection or production well to improve the recovery of the hydrocarbons, the type of tools to be used, the properties of the fluids used and recovered, and so on. These interpretations of reservoir models in terms of “operating technical parameters” are well known to the experts, despite the fact that new methods are regularly developed. Similarly, the modeling of CO2 storage sites makes it possible to monitor these sites, to detect anomalous behaviors and to predict the displacement of the injected CO2.
The purpose of a reservoir model is therefore to best reflect all the known information concerning a reservoir. A reservoir model is representative when a reservoir simulation provides estimates of historical data that are very close to the observed data. The term “historical data” is used to mean the production data obtained from measurements on the wells in response to the production of the reservoir (production of oil, production of water from one or more wells, gas/oil ratio (GOR), proportion of production water (“water cut”), and/or the repetitive seismic data (4D seismic impedances in one or more regions, etc.). A reservoir simulation is a technique that makes it possible to simulate the fluid flows within a reservoir by software called a flow simulator.
For this, the integration of all available data is essential. These data generally comprise:                Measurement at certain points of the geological formation, for example in wells. These data are called static because they are unchanging over time (in the reservoir production time scale) and are directly linked to the property of interest.        “Historical data” comprising production data, for example the fluid flow rates measured on the wells, the tracer concentrations and data obtained from seismic acquisition campaigns reiterated at successive intervals. These data are called dynamic because they change in the course of operation and are indirectly linked to the properties assigned to the meshes of the reservoir model.        
The techniques for integrating dynamic data (production and/or 4D seismic) in a reservoir model are well known to the experts: these are so-called “history matching” techniques.
History matching modifies the parameters of a reservoir model, such as the permeabilities, the porosities or the skins of wells (representing damage around the well), the connections of faults, and so on, to minimize the deviations between the simulated and measured historical data. The parameters may be linked to geographic regions, such as the permeabilities or porosities around a well or several wells. The deviation between real data and simulated data forms a functional, called an objective function. The history matching problem is resolved by minimizing this functional.
Many techniques have been developed over recent years to modify the geological model in order to match the historical data while preserving the consistency of this model with respect to the static observations. The available static data are used to define the random functions for each petrophysical property such as the porosity or permeability. A representation of the spatial distribution of a petrophysical property is a realization of a random function. Generally, a realization is generated from, on the one hand, a mean, a variance and a covariance function which characterizes the spatial variability of the property being studied and, on the other hand, a term or series of random numbers. There are many simulation techniques such as the Gaussian sequential simulation method, the Cholesky method or even the FFT-MA method.                Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation, Oxford Press, New York, 483 p.        Le Ravalec, M., Ncetinger B., and Hu L.-Y., 2000, The FFT Moving Average (FFT-MA) Generator: An Efficient Numerical Method for Generating and Conditioning Gaussian Simulations, Mathematical Geology, 32(6), 701-723.        
Perturbation techniques make it possible to modify a realization of a random function while ensuring the fact that the disturbed realization is also a realization of this same random function.
Among these perturbation techniques, there are the pilot points method developed by RamaRao et al. (1995) and Gomez-Hernandez et al. (1997), the gradual deformation method proposed by Hu (2000) and the probability perturbation method introduced by Caers (2003). These methods can be used to modify the spatial distribution of heterogeneities:                RamaRao, B. S., Lavenue, A. M., Marsilly, G. de, Marietta, M. G., 1995, Pilot Point Methodology for Automated Calibration of An Ensemble of Conditionally Simulated Transmissivity Fields. 1. Theory and Computational Experiments. WRR, 31(3), 475-493.        Gomez-Hernandez, J., Sahuquillo, A., and Capilla, J. E., 1997, Stochastic Simulation of Transmissivity Fields Conditional to Both Transmissivity and Piezometric Data, 1. Theory, J. of Hydrology, 203, 162-174.        Hu, L-Y., 2000, Gradual Deformation and Iterative Calibration of Gaussian-related Stochastic Models, Math. Geol., 32(1), 87-108.        Caers, J., 2003, Geostatistical History Matching Under Training-Image Based Geological Constraints. SPE J. 8(3), 218-226.        